Cremona's table of elliptic curves

17490 = 2 · 3 · 5 · 11 · 53

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 11- 53+	Signs for the Atkin-Lehner involutions
Class	17490l	Isogeny class
Conductor	17490	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	20480	Modular degree for the optimal curve
Δ	5028305040 = 24 · 34 · 5 · 114 · 53	Discriminant
Eigenvalues	2+ 3- 5+ -4 11-  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-609,4612]	[a1,a2,a3,a4,a6]
Generators	[-25:78:1]	Generators of the group modulo torsion
j	24920116376329/5028305040	j-invariant
L	3.8404255116005	L(r)(E,1)/r!
Ω	1.2930251308231	Real period
R	0.37126361855356	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52470bi1 87450bt1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 17490l1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	+	-4	-	6	-2	8	0	-2	-4	-6	-2	-12	0	+	4	-10	-12	12	6	-16	12	-6	-6

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Quadratic twists for elliptic curve 17490l1

-3	5
52470bi1	87450bt1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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